Recently, the study of modeling a non-stationary signal as a superposition of amplitude and frequency-modulated Fourier-like oscillatory modes has been a very active research area. The synchrosqueezing transform (SST) is a powerful method for instantaneous frequency estimation and component separation of non-stationary multicomponent signals. The short-time Fourier transform-based SST (FSST) reassigns the frequency variable to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. Very recently the FSST with a time-varying parameter, called the adaptive FSST, was introduced. The simulation experiments show that the adaptive FSST is very promising in instantaneous frequency estimation of the component of a multicomponent signal, and in accurate component recovery. However, the theoretical analysis of the adaptive FSST has not been carried out. In this paper, we study the theoretical analysis of the adaptive FSST and obtain the error bounds for the instantaneous frequency estimation and component recovery with the adaptive FSST and the second-order adaptive FSST.
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Xi An Jiao Tong Univ, Natl Engn Res Ctr Offshore Oil & Gas Explorat, Sch Informat & Commun Engn, Xian 710049, Peoples R ChinaXi An Jiao Tong Univ, Natl Engn Res Ctr Offshore Oil & Gas Explorat, Sch Informat & Commun Engn, Xian 710049, Peoples R China
Li, Zhen
Gao, Zhaoqi
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Xi An Jiao Tong Univ, Natl Engn Res Ctr Offshore Oil & Gas Explorat, Sch Informat & Commun Engn, Xian 710049, Peoples R ChinaXi An Jiao Tong Univ, Natl Engn Res Ctr Offshore Oil & Gas Explorat, Sch Informat & Commun Engn, Xian 710049, Peoples R China
Gao, Zhaoqi
Chen, Liang
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Jiujiang Univ, Dept Math, Jiujiang 332005, Peoples R ChinaXi An Jiao Tong Univ, Natl Engn Res Ctr Offshore Oil & Gas Explorat, Sch Informat & Commun Engn, Xian 710049, Peoples R China
Chen, Liang
Gao, Jinghuai
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Xi An Jiao Tong Univ, Natl Engn Res Ctr Offshore Oil & Gas Explorat, Sch Informat & Commun Engn, Xian 710049, Peoples R ChinaXi An Jiao Tong Univ, Natl Engn Res Ctr Offshore Oil & Gas Explorat, Sch Informat & Commun Engn, Xian 710049, Peoples R China
Gao, Jinghuai
Xu, Zongben
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Xian Jiaotong Univ Xian, Sch Math & Stat, Xian 710049, Peoples R ChinaXi An Jiao Tong Univ, Natl Engn Res Ctr Offshore Oil & Gas Explorat, Sch Informat & Commun Engn, Xian 710049, Peoples R China
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UNER, Inst Res & Dev Bioengn & Bioinformat, CONICET, RA-3100 Oro Verde, Entre Rios, Argentina
UNER, Fac Engn, RA-3100 Oro Verde, Entre Rios, ArgentinaUNER, Inst Res & Dev Bioengn & Bioinformat, CONICET, RA-3100 Oro Verde, Entre Rios, Argentina
Colominas, Marcelo A.
Meignen, Sylvain
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Univ Grenoble Alpes, Jean Kuntzmann Lab, Batiment IMAG, F-38401 St Martin Dheres, FranceUNER, Inst Res & Dev Bioengn & Bioinformat, CONICET, RA-3100 Oro Verde, Entre Rios, Argentina